C₁₁×#12419 #14589612

order	2816
nilpotency class	4
isoclinism	isoclinic class of #12416
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₁×#12419

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₁	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
prime radical	C₁₁×#493	C₂²
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈²×C₁₁ ◁ G

240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1408

A minimal faithful permutation representation — 3 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(21,24)(22,27)(23,26)(28,29)(30,35)(31,34)(32,33);(12,13,14,16,15,17,18,19)(20,21,26,29,25,28,23,24)(22,27,33,35,31,34,30,32);(20,22,25,31)(21,27,28,34)(23,30,26,33)(24,32,29,35)

Conjugacy classes & character table

473 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2816, 5407);